Japanese Patent Publication No. 1994/341527 shows a control method in which the period of time from the start of the torque phase to the inertia phase is detected at the time of shifting up and it is determined that a change with time exists in the friction engagement devices when the period of time has varied from a set value. The hydraulic pressures supplied to the two friction engagement devices are controlled so that overlapping of the torques born by the friction engagement device on the disengaging side and the friction engagement device on the engaging side is corrected. The torque phase is defined as a period during which the torque alone is varied while the engine speed remains unchanged at the start of shifting, for example, from second to third (hereinafter called 2-to-3 shifting), as indicated by temporal variations of a Gf signal (to be described later) in FIG. 2. Further, the period following the torque phase is called an inertia phase, in which the clutch inside the transmission starts to be engaged and the engine speed drops accordingly.
In another conventional method, such as the one disclosed in the gazette of Japanese Patent Laid-open No. Hei 6-341527, when it is attempted to detect the period of time from the start of the torque phase to the inertia phase at the time of shifting up in order to detect existence of a change with time in the friction engagement devices, it becomes necessary to store in memory the temporal data, which are required for detecting the change with time, for each of shifting, such as 1-to-2 shifting and 2-to-3 shifting and, further, for each of throttle openings. Therefore, there is a problem with such a method that the capacity of the ROM (Read Only Memory) of the microcomputer increases.